Using a plane wave expansion method, we numerically show that the bandgaps of honeycomb photonic bandgap fibers can be effectively tuned by interstitial air holes. It is shown that the number of bands varies with the filling fraction of interstitial air holes, and also that the width of the bands can be substantially increased by interstitial air holes. For a honeycomb photonic bandgap fiber with a large air filling fraction, the widths of the primary and secondary bandgaps are increased twice by interstitial air holes. In the case of a small air filling fraction, the relative sizes of the two gaps can reach up to 11.7% and 6.4% using interstitial air holes. Therefore, using interstitial air holes proves to be an effective way to tune the bandgaps of honeycomb photonic bandgap fibers.